Linear stochastic systems corrupted by Gaussian white noise disturbances are considered. An elementary proof of boundedness of the mean square response under a certainty equivalence minimum variance control law is described. The assumptions used in this ideal case indicate that the usual smallness in the mean conditions used in adaptive control could be overly restrictive. The methodology leads naturally to new performance bounds for such time-varying systems. Some simulations are presented to verify the results and to test the tightness of the assumptions used. >